The number of homeless in the city hit a record high last year, when 113,553 people passed through shelter programs — an 8 percent increase over 2009 that advocates blamed on a change in City Hall’s strategy for finding housing.

“The mayor’s failed policies have created a revolving door back into shelters, exacerbating the crisis and leading to record levels of homelessness in New York City,” said Patrick Markee, a senior policy analyst at the Coalition for the Homeless, which released its report yesterday.

The group faulted the Bloomberg administration for shifting away from the use of federal vouchers to place homeless families in housing in 2006. According to the coalition’s report, that move cost the city $370 million for 12,345 families that would have avoided the city-subsidized shelters. Bloomberg blamed the spike on the sluggish economy and improvements to the system.